Atkin and Lehner studied the theory of new forms of the space S<sub>2k</sub>（N） of cusp forms with group Γ<sub>0</sub>（N） and weight 2k and proved that S<sub>2k</sub>（N）=S<...Atkin and Lehner studied the theory of new forms of the space S<sub>2k</sub>（N） of cusp forms with group Γ<sub>0</sub>（N） and weight 2k and proved that S<sub>2k</sub>（N）=S<sub>2k</sub><sup>n</sup>ew（N）⊕S<sub>2k</sub><sup>o</sup>ld（N）and there exists a basis in S<sub>2k</sub><sup>n</sup>ew（N） which are eigenvectors for all Hecke operators but there exists a basis in S<sub>2k</sub><sup>o</sup>ld（N） which are eigenvectors for only those Hecke operators T（p）((p,展开更多
文摘Atkin and Lehner studied the theory of new forms of the space S<sub>2k</sub>（N） of cusp forms with group Γ<sub>0</sub>（N） and weight 2k and proved that S<sub>2k</sub>（N）=S<sub>2k</sub><sup>n</sup>ew（N）⊕S<sub>2k</sub><sup>o</sup>ld（N）and there exists a basis in S<sub>2k</sub><sup>n</sup>ew（N） which are eigenvectors for all Hecke operators but there exists a basis in S<sub>2k</sub><sup>o</sup>ld（N） which are eigenvectors for only those Hecke operators T（p）((p,
